1. Field of the Invention
The invention pertains to the field of pore structure characterization. More particularly, the invention pertains to a method and apparatus for determination of the diameter, volume and distribution of pores in hydrophobic porous materials.
2. Description of Related Art
Various porous materials currently are being developed and used for applications in a wide variety of industries, including, for example, fuel cells, biotechnology, filtration, and the household, hygienic and apparel industries, to name but a few. Many of these novel porous materials are hydrophobic in nature. These water repellent materials come with a wide range of pore sizes and physical characteristics. The pore structure characteristics of such materials, such as, for example, pore volume, pore diameter and pore distribution of the materials, often are required for a useful evaluation of the materials' quality and performance.
Many applications of such hydrophobic porous materials often require the materials to operate under compressive stress (e.g., filtration and fuel cells are common examples). Therefore, the influence of compressive stress on the pore structure characteristics of the porous materials often is required to evaluate the suitability of the materials for various applications. Thus, there is a strong need in the art for the development of suitable technology to measure the pore structure characteristics of hydrophobic materials, particularly while such materials are subjected to compressive stress. Pore structure characteristics in the x-y plane determine the performance of a number of materials in application. For example, in materials used in the manufacture of diapers, in-plane permeability and liquid intakes are important. Previously, there was no available technique for measurement of in-plane pore volume. Thus, there is a strong need in the art for the development of suitable technology to measure the pore structure characteristics of hydrophobic materials in the x-y plane.
U.S. Pat. No. 7,210,335 discloses an automated clamp-on sample chamber for flow porometry and a method of using same. The sample chamber includes a movable upper chamber. The movable upper chamber includes a center bore opening to a bottom of the chamber, at least one port for introduction of gas under pressure to the center bore, and a first annular seal around the center bore. A stationary lower seat opposing the upper chamber has a center bore aligned with the upper chamber, and includes an exhaust and a second annular seal around the center bore. A test material is placed between the upper chamber and the lower seat. An actuator moves the upper chamber. When the upper chamber is moved down with the first annular seal in contact with an upper surface of a sample of the material and the second annular seal in contact with a lower surface of the sample, gas introduced to the upper chamber goes through the sample and out through the exhaust. Measured differential pressures and gas flow rates yield pore diameter, pore distribution, and permeability.
U.S. Pat. No. 6,655,192 discloses a permeameter-porosimeter for providing normal and lateral permeability measurements on porous materials. The permeability measurements can be made on compressed or uncompressed samples and can be made at room temperature or at elevated temperatures. A wide variety of fluids, gas or liquid, can be used as the penetrating test fluid, depending on the application and the porosity of the porous sample. The penetrating test fluid is forced through the sample under pressure. The load, the fluid displacement, and the time are recorded and used in the calculations of permeability, porosity, pore size distribution, average pore size and the number of pores per unit area.
U.S. Pat. No. 6,178,808 discloses a method for measuring hydraulic conductivity of geological samples, using a closed volume pumping system that ensures constant volume of test liquid within the sample, and a shaped tube of mercury to provide a constant pressure difference across the sample to eliminate second order influences on the hydraulic conductivity measurement and to speed measurement.
U.S. Pat. No. 5,394,737 discloses an apparatus for testing the permeability of shredded elastomeric material, which contains a vessel, a bed of tire chips in the vessel, and a fluid inlet which communicates with a first fluid outlet and a second fluid outlet through the bed of tire chips. The first fluid outlet is provided with a cap for optionally preventing fluid flow through it. The second fluid outlet is higher than both the fluid inlet and the first fluid outlet. A plate located above the bed of tire chips is used to compress the tire chips.
U.S. Pat. No. 3,577,767 discloses a felt permeability testing apparatus. Various permeability characteristics of a sample of felt or other permeable web materials are determined by testing apparatus comprising a pair of interchangeable platens between which the sample is subjected to controlled compression, as a measured flow of liquid is forced through the sample from one platen to the other, along a predetermined flow path established by the particular pair of platens installed in the apparatus.
Japanese Patent Publication No. 02268249 discloses a water permeability testing method to facilitate the computation of water permeability coefficients in a short time, by laminating a sample to be measured with measuring samples whose permeability coefficients are larger than that of said sample, forming a test body, making water permeate into the test body, and measuring a unit quantity of permeation. A test body having a laminated structure is formed on a stage seat at the bottom of a pressure-proof container with the following materials: a sample to be measured whose thickness is thin and permeability coefficient is unknown, and measuring materials whose permeability coefficients are known and larger than that of the sample. Then water is infiltrated into the test body from a water feeding tank. The unit quantity of water permeation in a measuring buret is measured through a water pipe. The unit quantity of water permeation, the unit cross sectional area of the test body and a unit hydraulic grade are substituted for the terms of the equation of Darcy's law. Thus the permeation coefficient of the entire test body is computed. Then, the permeation coefficient of the sample to be measured is obtained, based on the permeation coefficient and the thickness of the entire test body, the thickness of the sample to be measured and the permeation coefficients of the measuring materials.
Mercury intrusion porosimetry is a well known technique widely used to measure pore size, pore volume, and pore volume distribution of porous materials, which are not wetted by mercury. In this technique, mercury is allowed to surround the non-wetting sample. The non-wetting mercury does not enter the pores of the sample spontaneously, rather, application of pressure on the mercury forces it to intrude into the pores of the sample.
The pressure required for intrusion of the non-wetting mercury into a pore is related to the diameter of the pore and is given by the following well known relation:(P−Pp)=−4γ cos θ/D  (1)where P is the intrusion pressure on the non-wetting mercury, Pp is the gas pressure in the pore, γ is the surface tension of the non-wetting mercury, θ is the contact angle of the non-wetting mercury with the sample, and D is the pore diameter.
The intrusion pressure is positive because the contact angle, θ, of a non-wetting liquid is greater than 90° and cos θ is negative. With increasing pressure, intrusion occurs into smaller pores. Intrusion pressures and intrusion volumes are then measured. Intrusion pressure gives pore diameter. At a given intrusion pressure, all pores larger than the pore corresponding to the intrusion pressure are filled with mercury. The intrusion volume at the intrusion pressure is the volume of all pores filled with mercury at the intrusion pressure.
The surface tension of mercury is 480 dynes/cm and the contact angle is 140°. The sample is evacuated before mercury surrounds the sample. Therefore, the pore diameter is computed taking Pp as zero. Typical differential pressures required to measure pore structure characteristics by mercury intrusion and water intrusion are shown in Table 1.
TABLE 1Pore diameterDifferential PressureDifferential Pressure(μm)of Mercury on pores (psi)of Water on pores(psi)0.001213,00020,9000.00542,7004,1800.01021,3002,0900.1002,130209121320.91021.32.092010.71.04504.270.4181002.130.2092001.070.104
Mercury intrusion porosimetry has a number of limitations. For example, the intrusion pressures for mercury intrusion are very high, particularly for small pores. High pressures tend to distort the pore structure and provide less reliable pore size distribution data. The large pores also are difficult to measure accurately, because the small pressures required are difficult to control accurately in the wide pressure range normally employed for the test, and further, because of the high density of mercury, large pores may get filled up due to pressure created by gravity. In-plane pore structure can not be measured by mercury intrusion porosimetry. Moreover, the effect of compressive stress on the sample on its pore structure cannot be determined by mercury intrusion porosimetry. Furthermore, mercury used in the test is toxic and is forbidden in many work environments. The sample also gets contaminated with mercury, cannot be reused, and must be properly disposed. Because of such limitations of this technique, mercury intrusion porosimetry is not effective in determining the pore structure characteristics of many materials of interest.
Water Intrusion Porosimetry is another known technique. Water does not enter the pores of hydrophobic materials spontaneously, rather, on application of pressure on water it enters the pores. In this technique, pressure is increased on water surrounding the sample. Intrusion pressures and intrusion volumes are measured. Intrusion pressure gives pore diameter. At a given intrusion pressure, all pores larger than the pore corresponding to the intrusion pressure are filled with water. The intrusion volume at the intrusion pressure is the volume of all pores filled with water at the intrusion pressure. The surface tension of water is 72 dynes/cm and the contact angle is often 120°. The sample is not evacuated before surrounding with water because of evaporation of water. The pore diameter is computed neglecting the pressure of gas in the pore, Pp and using the following relation, already cited above, and:(P−Pp)=−4γ cos θ/D  (2)where P is the intrusion pressure on the non-wetting water, Pp is the gas pressure in the pore, γ is the surface tension of the non-wetting water, θ is the contact angle of water with the sample, and D is the pore diameter. Typical pressures required for intrusion of water into the pores of hydrophobic materials are listed in Table 1.
However, as with mercury, the available technology for water intrusion porosimetry also has a number of limitations and disadvantages. Using the available technology for water intrusion porosimetry, pore structures of samples under compressive stress cannot be determined. Currently known methods for water intrusion porosimetry also cannot measure volume and diameter of pores in the x-y plane.
Another disadvantage of water intrusion porosimetry is that the air trapped in a pore prevents water from completely filling the pore. Thus, the pore volume occupied by the trapped air is not measured. Because of the relatively high pressure of the trapped air, a large part of the pore volume is not measured in large and small pores, and part of the pore volume of large pores is measured at much higher pressures. Furthermore, because of the pressure of the gas trapped inside the pores, higher differential pressure is needed for intrusion. Therefore, the computed pore diameter is less than the actual pore diameter. Although the error in the measured pore diameter generally is negligible for small pores, it is very high in the case of large pores, because of large relative pressures of the trapped air.
Yet another disadvantage of water intrusion porosimetry is that, when water surrounds the sample in the sample chamber for intrusion, the air present in the sample chamber is trapped in the sample chamber above the water. This air does not dissolve in the already air-saturated water. When the pressure of the water is increased for intrusion, the air trapped in the sample chamber is compressed. Water fills the space created by the decrease in volume of the trapped air in the sample chamber, due to compression of the trapped air, and the intrusion volume of the water is measured as the pore volume. This error can be appreciable for large and small pores, although part of it can be compensated by a blank run. In a blank run, the intrusion volume is measured as a function of differential pressure, without the sample, and the measured intrusion volume is subtracted from the measured intrusion volume of the sample. This procedure also corrects for errors due to the effect of compressibility of the liquid and expansion of the sample chamber. However, such corrections can be cumbersome and can introduce a significant source of error.
Hence, although there are known methods and apparatus that are intended to aid in the analysis of the pore structure characteristics of various porous materials, one problem with the known methods is that they are not well-suited for accurately analyzing the pore volume and pore diameter of hydrophobic porous materials, they are incapable of measuring pore volume and diameter of hydrophobic materials under compressive stress, and incapable of evaluating the pore volume and diameter of in-plane pores. Thus, there is a continuing need in the art for a method and apparatus suitable for accurately measuring the pore volume and diameter of hydrophobic materials under compressive stress and in the in-plane.